Question

4. Find GCD of p² +5p +6, p? +7p+12​

Answer 1

Step-by-step explanation:

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Answer 2

Given:

$\[{p^2} + 5p + 6,\]$ and $\[{p^2} + 7p + 12\]$

Solution:

Know that the GCD is greatest common number that completely divides the given numbers.

Factorize $\[{p^2} + 5p + 6,\]$

$\[\begin{array}{l} \Rightarrow {p^2} + 2p + 3p + 6\\ \Rightarrow p\left( {p + 2} \right) + 3\left( {p + 2} \right)\\ \Rightarrow \left( {p + 2} \right)\left( {p + 3} \right)\end{array}\]$

Factorize $\[{p^2} + 7p + 12\]$,

$\[\begin{array}{l} \Rightarrow {p^2} + 3p + 4p + 12\\ \Rightarrow p\left( {p + 3} \right) + 4\left( {p + 3} \right)\\ \Rightarrow \left( {p + 3} \right)\left( {p + 4} \right)\end{array}\]$

Hence, the GCD is  $\[\left( {p + 3} \right)\]$.